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FACTA UNIVERSITATIS (NIS)

SER .: ELE C. ENERG. vol. 23, no. 1, Apr. 2010, 73-88

Bandwidth Calculation for VoIP Networks Based on PSTN

Statistical Model

Zvezdan Stojanovic and D- ord-e Babic

Abstract: This paper shows an analysis how to calculate proper bandwidth for VoIP

calls after proper dimensioning of PSTN network. For this purpose, we use Erlang B

and extended Erlang B formulae. Further, we have developed a software tool, named

Bandwidth Calculator to calculate proper number of the circuits on the PSTN side and

after that IP bandwidth. Traffic analysis is conducted for VoIP networks consideringimpact of many factors on the bandwidth such as: voice codecs, samples, VAD, RTP

compression. The results obtained by bandwidth calculator are compared to simula-

tion results and data obtained by measurements.

Keywords: VoIP, bandwidth calculation, tele-traffic analysis.

1 Introduction

BANDWIDTH is probably the most expensive component of the network. The

network administrator has to know how to calculate proper bandwidth and

how to reduce overall bandwidth consumption [13]. In this paper we develop

a method to calculate proper bandwidth for VoIP calls after proper dimensioningPSTN network and determining optimal number of the circuits for the peak hour

time.

In this paper, the two categories of Internet subscribers are considered: dial-

up and ADSL. In the Literature ( [411]), it is assumed that the Internet traffic

has property of self-similarity. In order to express the degree of self-similarity

numerically, we use so-called Hurst parameter. In [4] and [6] it has been shown

that when value of Hurst parameter is small, i.e. H< 0,7, a classical model can

Manuscript received on January 13, 2010.

Z. Stojanovic is with Telekom Srpske, Bosnia and Herzegovina (e-mail:

[email protected]). Dj. Babic is with Faculty of Information Technology,

Slobomir P University, 76300 Bijeljina, Bosnia and Herzegovina (e-mail: [email protected]).

73


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74 Z. Stojanovi c and D- . Babi c:

be used, which is based on Erlang B and Extended Erlang B and their inversion

functions. Thus, our first task is to check if classical method for calculation of

number of circuits can be used. This can be done by calculating Hurst parameter

for both type of traffic. Here, we use linear and square regression to show future

trends of the ADSL and dial-up traffic behaviors and for the calculation of Hurst

parameter.

The main task is to find method for proper dimensioning of a typical PSTN

network. We consider a typical part of the network; however results and tools can

be applied to any similar situation. We show that the value of Hurst parameter is in

range H< 0.7 for dial-up traffic and for ADSL traffic is bigger than 0.7 . Erlangbased model can be applied for the network with low load and rare loss and for the

high speed and highly aggregated traffic on the backbone network (network core)

because that traffic tends back to Poisson [1216] . Because of its mathematical

simplicity, well defined and well-known conditions for the simulations, it is still

useful tool [1319].

Further, obtained traffic analysis is applied to VoIP network, and proper band-

width for VoIP calls is calculated. We have developed a software tool which op-erates as bandwidth calculator for such network [19]. First, we calculate proper

number of circuits. After that, based on this calculation, the proper bandwidth

is calculated for several VoIP codecs. The bandwidth calculation takes into con-

sideration impact of many factors on the bandwidth such as: voice codecs, VAD,

RTP compression. The results obtained by bandwidth calculator are compared to

simulation results and data obtained by measurements.

The paper is organized as follows. In chapter 2, PSTN statistical model is

described. The regression analysis is made in Chapter 3. Tele-traffic analysis is

presented in Chapter 4. Finally, some case studies are discussed in Chapter 5.

Chapter 6 describes traffic analysis of the VoIP network.

2 PSTN Statistical Model

Erlang B and Extended Erlang B models are used to determine proper number

of circuits to carry voice traffic during the busy hour time (BHT), because it is

period with maximum traffic load which one network must support [20]. However,

our aim is to calculate proper number of circuits for VoIP calls. In determining

busy hour traffic (BHT) intensity for certain day, we have to use simplification

in which BHT is 17 percent of all traffic for that day [21]. The Erlang B traffic

model [1924] is based on the following initial assumptions: (i) an infinite number

of sources, (ii) Poisson arrival process, (iii) block calls cleared, and (iv) holding

times are exponentially distributed. But it can be shown that (iv) assumption is


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Bandwidth Calculation for VoIP Networks Based on PSTN Statistical Model 75

valid for arbitrary holding time distribution [20,22]. In this paper is checked which

distribution is valid in our case.

The following expression is used to derive the Erlang B model:

PB =

Aci

c!c

k=1

Ak

k!

(1)

Here, PB is the probability of blocking a call, c is number of circuits, and Ai is

offered Internet traffic1. Calls with retrials are not used into the consideration in

Erlang B model. For this purpose Extended Erlang B model is used which can be

calculated on the base of already calculated Erlang B model. Based on (1), Erlang

B, Extended Erlang B models and their inversion functions, we have developed the

software tool named Bandwidth Calculator [19]. The Bandwidth Calculator can

be used to determine proper number of circuits for VoIP calls. The user interface

of the software tool is shown and explained later.

Erlang based model can be applied for the network with low load and rare loss

and for the high speed and highly aggregated traffic on the backbone network (net-

work core) because that traffic tends back to Poisson. Because of its mathematical

simplicity, well defined and well-known conditions for the simulations it is still

useful tool [1319].

3 Regression Analysis

In order to analyze how increased number of subscribers influence on the traffic and

to calculate Hurst parameter, we use regression model for the specific category of

subscribers under consideration. The regression analysis is used to examine trends

of the subscriber behavior in the future. We use regression analysis model which

is based on the real values of the variables obtained by measurements. The regres-

sion analysis includes estimation of the unknown parameters, calculating dispersion

characteristics and other statistical-analytical indices [25,26].

The regression model is used when it is desired to express analytical relation

between data appearance. The aim of this model is to find relationship between

single variable Y and several variables X. The simplest method of the regression is

linear regression [25]:

Y = a + bX+ u (2)

1Offered traffic is theoretical parameter, it can not be measured and it is used for calculation like

in Erlang formula. Calculations on the rest of the paper is based on the real, measured traffic known

as carried (serverd) traffic.


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Here, X is independent variable, Y is dependent variable, u is error term known as

residual, and a, b are parameters which have to be determined. Equation (2) can be

written as:

yi = yi + ui, where yi = a + bxi, for i = 1,2,...,n. (3)

where, yi is a deterministic part of model. Residual ui can be expressed as:

ui = yi yi, ui = yiabxi, for i = 1,2,...,n. (4)

In order to achieve better accuracy, square regression and method of the least

squares can be used: The square regression model is expressed as [24]:

yi = a + bxi + cx2 + ui, for i = 1,2,...,n. (5)

Residual sum of squares can be written as:

SQ =n

i=1

(yi yi)2 =

n

i=1

(yi (a + bxi + cx2i ))

2. (6)

Parameters a,b and c can be found by solving the following set of equations:

SQ

a= 0;

SQ

b= 0;

SQ

c= 0 (7)

Mathematical calculations are performed by using Matlab and by operating with

data obtained by measurements.

4 Tele-Traffic Analysis

When setting up a statistical model of a network, it is very important to chooseproper mathematical traffic model. For connection-oriented circuit switched appli-

cation, such as voice, relatively simple analytical model exists based on the Poisson

process. This is classical model [20]. Connectionless packet-oriented data traffic

(Internet traffic) is much more variable and thus less predictable. The main rea-

son is in the fact that a typical multimedia application contains packets from the

different sources, such as video, voice and data, which differ in statistical pattern.

However, the traffic poses certain degree of correlation between arrivals and long

range dependences on time, thus it can be defined as self-similar traffic [9], [10].

The fundamental questions related to the traffic model are:

1. Whether it is possible to use the classical model in the presence of self-

similar traffic, and,


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2. How self-similarity influences on the network performance in the situation

under consideration.

In this paper, the property of self-similarity and Hurst parameter which is used to

measure degree of self similarity is explained. After that, self-similarity of dial-upand ADSL traffic are analyzed, for the network segment under consideration. All

analysis and other calculations are performed using traffic measurements in a real

network.

4.1 Self-similar traffic

A self-similar phenomenon displays structural similarities across a wide range of

timescales: milliseconds, seconds, minutes, hour, even days and weeks. It means

that it is not matter what time scale is observed, similar pattern is seen (fractal-like

behavior) [4]. The definition of self-similarity is given below [4,6, 9,10]:X is defined to be a wide sense stationary random process with mean ,

variance and autocorrelation function r(k). A stationary random process X =(Xt; t = 1,2,3.) is statistically exact second-order self-similar if it has the sameautocorrelation function r(k) = E[(xt )(xt+1 )] as the series X

m for all m,

where Xm is the m-aggregated series X(m) = (X(m)k

; k = 1,2,3,...) obtained by

summing the original series X over non-overlapping blocks of size m, X(m)k =

1m

(Xkmm+1 +Xkmm+2 + +Xkm).

The self-similar process has the following properties: i) slowly decaying vari-

ance, and ii) long range dependence. Hurst parameter H is used to determine the

degree of the self-similarity. It expresses the speed of decay of the autocorrelation

function. For a self-similar process, Hurst parameter is in range 12< H< 1; for

H = 12

the time series is short range dependent; for H 1, the process becomes

more and more self similar [4]. In [4] and [6], it is shown that for H< 0,7, thelong-range dependence is unimportant, and self-similar traffic pattern can be ne-

glected. In this case classical model for traffic engineering can be used. This type

of traffic has short-range dependency.

For the larger values of Hurst parameter H, the property of self-similarity has

bad influence on the network performance. In [5], it is shown that in this case,

buffering can be extremely large. However, increased buffering leads to large queu-

ing delays and overall delay which has impact on QoS for real-time applications,

e.g. for VoIP. In the case under consideration, H parameter has to be calculated for

the dial-up and ADSL traffic.


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4.2 R/S method for the calculation of Hurst parameter

In [6], [8] and [9], several methods for calculation of Hurst parameter are explained.

However, in this paper, we use R/Smethod.For empirical time series Xt (for t = 1,2,...,n) with arithmetic mean X(n) and

variance S2

(n), we define R/Sstatistics, also called Rescaled Adjusted Range, withR(n)/S(n) [9]. Here R(n) is defined as:

R(n) = max

n

i=1

(XiX(n)), 1 k n

min

n

i=1

(XiX(n)), 1 k n

(8)

For almost all naturally occurring time series, the rescaled adjusted range statistic

for set of samples of size n follows the following relationship:

E

R(n)

S(n)

cnH as n , c is constant. (9)

If log[R(n)/S(n)] is plotted versus log(n), the slope of the curve is equal toHurst parameter H.

5 Case Studies

In this part, we consider a typical part of the network; however results and tools

can be applied to any similar situation.

5.1 Description of the network segment under consideration

Figure 1 shows situation under analyses. From Fig. 1, it is obvious that there are

two types of the traffic which must be observed differently.

1. Served (carried) dial-up traffic: It can be seen from the Fig. 1. that sub-

scribers from Tandem Office (TO in Fig. 1.) use same circuits for voice and

data for transmission to the Main Exchange (ME in the Fig. 1.) in Zvornik for

dial-up category of the subscribers. The switching part of EWSD exchange

in Zvornik (ME in Fig. 1.) separates voice from data using dialed numbers.

This is done due to the fact that anonymous dial-up subscribers dial 081-50-

1433 and classical dial-up subscribers dial 081-59-1432 number, and thus

all subscribers dialing those numbers are directed to Access Server. Access

Server and switching part of EWSD exchange are connected via 90 transmis-

sion trunks. After that data is transferred to IP-MPLS bus across edge router.

All traffic between main exchange and all exchanges which are connected to

the main exchange is measured.


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Fig. 1. Network segment under consideration

2. Served (carried) ADSL traffic (data part of ADSL traffic): From each Node

Exchange (NE) and TO with ADSL to the ME (Main Exchange), see Fig. 1,

data part of ADSL traffic is transmitted using separate optical transmission

network. The voice part of the ADSL traffic from all exchanges is mixed

with voice traffic, from ordinary PSTN subscribers [19]. Whole data part of

ADSL traffic, from NE, TO and ME, is directed via edge router in Zvornik

to IP/MPLS bus to core router in Banja Luka.

Overall served traffic is composed of served telephone and data traffic:

Amix = At +Ai (10)

Here, Amix is overall served traffic, At is served telephone traffic and Ai is served

Internet (data) traffic. In our case:

Ai = Adial up +AADSL. (11)

In (11), Ai is served data traffic directed from edge router in Zvornik to core

router in Banja Luka by GEth (Zx) interface, and

Adial up = Adial up 56k+Adial up ISDN (12)


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where, Adial up 56k is served traffic from subscribers with dial-up connections to

Internet, and Adial up ISDN is served traffic from subscribers with ISDN connection

to Internet and AADSL is served traffic from ADSL subscribers [19].

ADSL served traffic and dial-up served traffic are different, by their nature,

because ADSL served traffic has bigger self-similarity than dial-up served traffic

which can not be neglected. ADSL served traffic has different statistical properties.The third difference is the fact that data part of ADSL served traffic is directed

permanently to IP/MPLS bus. The rest of traffic, i.e. dial-up served traffic and voice

served traffic, which come to main exchange from all NEs, (Node Exchanges),

TO and RDLU (Remote Digital Line Unit) is directed to the IP/MPLS bus after

separation of voice and data, see Fig. 1.

Having in mind the self-similarity property of ADSL traffic and the fact that

IP/MPLS bus has great capacity and DWDM equipment is ready to start with

works, there is no sense to perform dimensioning of that part of the network. Sta-

tistical models used here are based on real data obtained by measurement of traffic

between Access Server and edge router.

5.2 Traffic variables

There are two key traffic variables for dial-up traffic: holding time and interarrival

time [27,28]. In order to test initial assumption that holding time is exponentially

distributed according to Erlang B model, we take only first variable in considera-

tion. There are several methods to examine the underlying distribution [28]. In this

paper, we use two: i) a histogram or density plot, and, ii) the squared coefficient of

variance.

In order to test assumption of underlying distribution, we use data obtained by

measurements during 6 months. Based on the collected data, it is very useful to plot

frequency of occurrence of each score. This is known as frequency distribution, orhistogram, which is simply a graph plotting values of service times (holding times),

on x axis, and number of observations (frequency) on y axis. In ideal case, i.e. in

the case of normal distribution, all service times will be distributed symetrically

around the centre of all values (peak value at the mean). However, from Fig. 2, we

see that this is not the case.

From Fig. 2, we can see that a positive skew is evident in the data. This

implies that there are a many short sessions with short serving times. The large

number of short sessions can be based on large number of aborted sessions. A

histogram or density plot is more visual test and additional test has to be performed

to examine distribution. The squared coefficient of variance C2x is calculated to

provide additional information about underlying distribution [27].

From Table 1, one can be read data about variance (column 8), mean duration of


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Fig. 2. Histogram of the aggregate holding times (based on data obtained by measurements from

august 2008 to January 2009)

session (column 3) and square coefficient of variance (column 9). If squared coef-

ficient of variance is equal to one, i.e. C2x = 1, then X has exponential distribution.IfC2x = 1/k, then X has Erlang-k distribution. Finally, ifC

2x > 1, than X has n-

stage hyper-exponential distribution. The squared coefficient of variance (column

9) indicates that the services time follows hyper-exponentially distribution2 [28].

Table 1. Daily Service Time Statistics

Average

Numbers

of

Sessions

Mean

(sec)

Standard

Deviation

25%

Q3

50%

Me-

dian

75%

Q1 VarianceC2X

Monday 979,00 643,25 1.489,51 47 167 616 2.180.630 5,36

Tuesday 961,00 588,62 1.373,00 44 132 564 1.885.139 5,44

Wednesday 945,00 598,88 1.291,33 42 130 573 1.667.536 4,65

Thursday 971,00 621,78 1.498,38 40 146 592 2.245.164 5,81

Friday 945,00 614,40 1 .467,29 47 138 584 2.152.931 5,70

Saturday 821,00 622,87 1.617,34 52 129 552 2.615.778 6,74

Sunday 808,00 637,38 1.425,07 54 130 590 2.030.814 5,00

From Table 1, we see that the mean holding times per day are slightly different,

with the biggest value on Monday. In our case median holding time provides a little

more insight into actual traffic [26,28]. Based on the median value, we conclude

2Important properties of Erlang B formula is insensivity of underlaying distribution


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that 50 percent of all sessions involve short holding times. Seventy-five percent

of all sessions are less than 10 minutes in duration, and twenty-five percent of all

session are between one half and one minutes. These results are in accordance with

histogram in Fig. 2 and positive skew in it.

5.3 Self-similarity and Hurst parameter

In analysis of the dial-up traffic, we have used data obtained by traffic measurement

during 17 months for the network segment under consideration, see Fig. 1. In

analysis of ADSL traffic, we have used data obtained by traffic measurement during

8 months.

From Fig. 3.(a), we can see that the value of Hurst parameter for dial-up traffic

is H = 0,6344. We can conclude that in the case of dial-up traffic we can use clas-sical model for network dimensioning because H< 0,7. This fact is in accordancewith results of [4] and [6].

(a) (b)

Fig. 3. (a) R/S plot for dial-up traffic and, (b) ADSL traffic

From Fig. 3.(b), we can see that H = 0,8529, thus Hurst parameter is biggerthan 0,7. We can conclude that in the case of ADSL traffic the property of self-

similarity is significant, thus it is not possible to use classical model for network

dimensioning.

5.4 Network dimensioning and Bandwidth calculator

Figures from 4(a) to 4(b) show relationship between blocking probability PB and

recall factor (repeated call attempt), which is varied in the range from 0.1 to 0.9,

for each of 20 measured days, (table 2).


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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.5

1

1.5

2

2.5

3

Recall factor

Blockingprobability

Relationshiprecall factor to blocking probability

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Recall factor

Blockingprobability

Relationshiprecall factor to blocking probability

(a) (b)

Fig. 4. Relationship between blocking probability and recall factor for the constant number of trunks

(from 39 in (a) to 42 in (d)).

Table 2. Served traffic for 20 days in ME Zvornik

Day/Year Served Voice and Data TrafficBHT (in Erlang)

Served Data Traffic BHT (inErlang)

15Dec08 74,30 26,70

16Dec08 70,10 25,19

17Dec08 74,80 26,88

18Dec08 69,20 24,87

19Dec08 74,30 26,70

22Dec08 75,90 27,27

23Dec08 76,20 27,38

24Dec08 74,60 26,81

25Dec08 75,90 27,27

26Dec08 76,20 27,38

19Jan09 66,10 27,77

20Jan09 71,60 30,08

21Jan09 67,60 28,40

22Jan09 67,20 28,23

23Jan09 68,20 28,65

26Jan09 72,50 30,46

27Jan09 70,00 29,41

28Jan09 64,60 27,14

29Jan09 66,80 28,06

30Jan09 70,70 29,70

The measurements are performed in ME Zvornik exchange. From Fig. 4(a),

it can be seen that for the two days probability PB is larger than 2%, therefore we

must enlarge number of circuits. Hence, when the number of blocking the circuits


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is 42, as shown in Fig 4(b), blocking probability PB is less then 1%. This result

corresponds to the result which is obtained from the Bandwidth calculator. From

Fig. 4(b), it is obvious that for the maximum served traffic of 30.46 Erlangs and

blocking probability PB of 1%, we obtain same result as from bandwidth calculator,

which is shown in Fig. 7.

Fig. 5. Relationship between blocking probabil-

ity and recall factor for the max. served traffic

for 20 days in ME Zvornik (30,46 Erlangs)

1500 2000 2500 3000 3500 4000 450015

20

25

30

35

40

45

Servedtraffic(Erlang)

Number of subscribers per months

Relationshipnumber of subscribers to served traffic

Fig. 6. Relationship between number of sub-

scribers and measured traffic for dial-up sub-

scribers

Figure 5 shows relationship between blocking probability PB and recall factor,

which is varied in the range from the 0.1-0.9, for the maximum served traffic of the

30.46 Erlangs. The results are tested versus different number of circuits ranging

from 37 to 42. It is obvious from Fig. 4(b) and Fig. 5 that for the maximum served

traffic of 30.46 Erlangs and blocking probability PB of 1%, we obtain same result

as from Bandwidth calculator, which is shown in Fig. 7.

Figure 6 shows relationship between calculated parameters of square regres-

sion, dashed curve in Fig. 6, and real data obtained from the billing system, solid

curve in Fig. 6. The parameters of regression model are estimated using data

obtained by measurements. Matlab is also used to check results obtained by Band-

width Calculator and this is shown in Fig. 7.

6 Applaying Traffic Analysis to VoIP Networks

After proper dimensioning of PSTN network, the next task is to determine the por-

tion of bandwidth on the link between switching part of the ME exchange and

Access Server (see Fig. 1) that is used for VoIP. In this analysis, we consider influ-

ence of different Voice codecs, which are supported by Access Server, and Voice

Activity Detection (VAD) on the bandwidth for VoIP call. The Access Server sup-

ports the following VoIP codecs: G.711, G.729, G.723 and G.726. By increasing


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Fig. 7. Bandwidth calculator

number of voice samples per frame, the required bandwidth is decreased because

overall amount of headers required is reduced for the call. But this can increase

voice delay and decrease voice quality [1,2]. The number of voice samples to be

sent per frame depends on the type of codec that is used. It also depends on the

ratio: high resolution and high bandwidth (20 ms sample duration) or lower reso-

lution and lower bandwidth (50 ms sample duration) [3]. Default settings for all

codecs are shown in Fig. 7. Typical voice conversation can contain from 35 up to

50 percent of silence. VAD sends RTP packets only when voice is detected. For

VoIP bandwidth planning, it is assumed that VAD reduces bandwidth by 35 per-

cent; this fact is used in the Bandwidth calculator [19]. The results obtained by

Bandwidth calculator are displayed in Fig. 7.

The switching part of the ME exchange is connected to the Access Server by

Ethernet network, and that is why Ethernet as L2 layer is considered in bandwidth

calculator. PPP is also considered as L2 layer, thou procedure of the calculation for

any L2 is same. The only difference is the packet size which corresponds to certain


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L2 layer and consequently all other calculations follow this change. The protocol

cRTP can be used with PPP to compress IP/UDP/RTP header to two or four bytes.

This functionality is not supported in Ethernet [29]. Bandwidth per connection

for a single VoIP call (with and without VAD) is calculated and it is shown in

the 11th and 12th columns of Fig. 7. In Fig. 7, in the last two columns the overall

bandwidth (with and without VAD) is shown. This is required bandwidth to supportall calls during the peak hour. The overall bandwidth is product of the number of

circuits calculated for the traffic in peak hour (BHT in Fig. 7) for the some blocking

probability and bandwidth per connection. This represents full-duplex bandwidth

or bandwidth required in both directions.

7 Conclusion

The bandwidth is probably the most expensive component of the network. This pa-

per has shown a way how to calculate proper bandwidth for VoIP calls after proper

dimensioning PSTN network and determining optimal number of the circuits. The

model incorporated in software tool which works as bandwidth calculator is vali-

dated by simulation results in Matlab. We have used as an example a segment of

Telekom Srpskes network for which we have enough data. However, calculation

will be very alike for another provider or group of subscribers using leased lines for

Internet access and who want to save resources with proper determining bandwidth

for their purposes.

References

[1] J. Davidson, J. Peters, M. Bhatia, S. Kalidindi, and S. Mukherjee, Voice over IPFundamentals. New York: Cisco Press, 2006.

[2] B. Goode, The Jaumann structure in wave-digital filters, Proceedings of the IEEE,vol. 90, no. 9, pp. 14951517, Sept. 2002.

[3] Anonymous, Voice over IP-Per Call Bandwidth Consumption. New York: CiscoPress, 2005.

[4] Z. Sahinoglu and S. Tekinay, On multimedia networks: Self-similar traffic and net-work performance, IEEE Communications Magazine, vol. 37, pp. 4852, Jan. 1999.

[5] K. Park, G. Kim, and M. Crovella, On the effect of traffice self-similarity on networkperformance, in Proc. of SPIE International Conf. on Performance and Control ofNetwork System, Philadelphia, Pennsylvania, Nov. 1997, pp. 293310.

[6] T. R. Staake, IP traffic statistic-a markovian approach, Ph.D. dissertation, Worch-ester Polytechnic Institute, May 2002.

[7] P. H. P. de Carvalho, H. Abdalla, A. M. Soares, P. S. Barreto, and P. Tarchetti, Analy-sis of the influence of self-similar traffic in the performance of real time applications,

in The IAESTED, International Conference on Automation, Control and InformationTechnology, Novosibirsk, Russia.


15/16


[8] M. Gospodinov and E. Gospodinova, The graphical methods for estimating hurstparameter of self-similar network traffic, in International Conference on ComputerSystems and Technologies CompSysTech, Veliko Trnovo, Bulgaria.

[9] W. E. Leland, W. Willinger, M. S. Taqqu, and D. V. Wilson, On the self-similarnature of ethernet traffic, in Proc. ACM SIGCOMM.

[10] M. E. Crovella andA. Bestavros, Self-similarity in world wide web traffic: Evidence

and possible causes, Boston University, Aug. 1995.

[11] D. P. Heyman and T. V. Laksman, What are the implications of long-range depen-dence for VBR-video traffic engineering, IEEE Trans Networking, vol. 3, pp. 301317, Mar. 1996.

[12] N. Wisitpongphan and N. M. Peha, Effect of TCP on self-similarity of network traf-fic, in Proceedings of the 12th IEEE International Conference on Computer Com-munications and Networks (ICCCN), Dallas, USA, Oct. 2003, pp. 370373.

[13] A. Kos and J. Bester, Poisson packet traffic generation based on empirical data,Journal of systemics, cybernetics and informatics, vol. 1, pp. 14, May 2003.

[14] H. Jiang and C. Dovrolis, A nonstationary poisson view of internet traffic, in Pro-ceedings of IEEE INFOCOM, Hong Kong, China.

[15] M. F. T. Karagiannis, M. Molle, and A. Broido, Source-level IP packet bursts:Causes and effects, in Proceedings of Internet Measurement Conference (IMC), Mi-

ami, USA, Oct. 2003.[16] V. Grout, S. Cunningham, D. Oram, and R. Hebblewhite, A note on the distribution

of packet arrivals in high-speed data networks, in Proceedings of IADIS Interna-tional Conference, Madrid, Spain, Oct. 69, 2004.

[17] V. J. Ribeiro, Z. L. Zhang, S. Moon, and C. Diot, Small-time scaling behaviors ofinternet backbone traffic, Computer Networks.

[18] J. Cao, W. S. Cleveland, D. Lin, and D. X. Sun, The effect of statistical multiplexingon the long-range dependence of internet packet traffic, Tech. Rep., 2002.

[19] Z. Stojanovic and D. Babic, Traffic engineering for VoIP network based on PSTNstatistical models, in 9th IEEE International Conference on Telecommunications inModern Satellite, Cable and Broadcasting Services, TELSIKS, Nis, Serbia, Oct. 79,2009, pp. 564568.

[20] V. B. Iverson, Teletraffic engineering handbook, Ph.D. dissertation, Technical Uni-versity of Denmark, June 2006.

[21] Anonymous, Traffic Analysis for Voice over IP.

[22] M. B. Bakmaz and Z. S. Bojkovic, Uticaj erlangovih istrazivanja na razvojteorije telekomunikacionog saobracaja, in 15th Telekomunikacioni forum TELFOR,Beograd, Serbia, Nov. 2007, pp. 5662.

[23] R. B. Cooper and D. P. Heyman, Teletraffic Theory and Engineering, Froehlich/KentEncyclopedia of Telecommunications.

[24] A. A. Kist, Erlang b as a performance model for IP flows, in IEEE InternationalConference on Networks (ICON 2007), Adelaide, Australia, Nov. 2007.

[25] I. Sosic and V. Serder, Uvod u statistiku. Zagreb: Skolska knjiga, 2000.

[26] A. Field, Discovering Statistics Using SPSS. University of Sussex, 2007.

[27] J. Farber, S. Bodamer, and J. Charzinski, Statistical evaluation and modeling of In-ternet dial-up traffic. University of Stuttgart, Institute of Communication Networks

and Computer Engineering (IND) and Siemens AG, Information and CommunicationNetworks Group, 1999.


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[28] D. C. Novak, A methodology for characterization and performance analysis ofconnection-based network access technologies, Ph.D. dissertation, Virginia Poly-technic Institute and State University.

[29] H. Toral-Cruz and D. Torres-Roman, Traffic analysis for IP telephony, in 2nd In-ternational Conference on Electrical and Electronics Engineering (ICEEE) and XIConference on Electrical Engineering (CIE 2005)IEEE International Conference on

Networks (ICON 2007), Mexico City, Sept. 2005, pp. 136139.

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